55.24.43 problem 43

Internal problem ID [13672]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, section 1.3. Abel Equations of the Second Kind. subsection 1.3.3-2.
Problem number : 43
Date solved : Sunday, October 12, 2025 at 04:25:31 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y y^{\prime }+\frac {a \left (33 x +2\right ) y}{30 x^{{6}/{5}}}&=-\frac {a^{2} \left (x -1\right ) \left (9 x -4\right )}{30 x^{{7}/{5}}} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 4330

ode:=y(x)*diff(y(x),x)+1/30*a*(33*x+2)/x^(6/5)*y(x) = -1/30*a^2*(x-1)*(9*x-4)/x^(7/5); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {Expression too large to display} \]

✗ Mathematica

ode=y[x]*D[y[x],x]+1/30*a*(33*x+2)*x^(-6/5)*y[x]==-1/30*a^2*(x-1)*(9*x-4)*x^(-7/5); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(a**2*(x - 1)*(9*x - 4)/(30*x**(7/5)) + a*(33*x + 2)*y(x)/(30*x**(6/5)) + y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out